Password Lockouts

Recently a site I’ve had up and running for a while starting exhibiting an odd behavior. Each time a user logs out and closes their browser, the site refuses their password on the next login attempt.

Steps I’ve taken to resolve the issue:
Cleared browser cache – no luck.
Attempted with Firefox, Safari and Chrome – no luck.
Used MyPHPAdmin and changed passwords (set w/MD5) – no luck.
Disabled all plug-ins – no luck.
Set the theme to twenty-ten – no luck.
Dumped the database, created a new on and restored it – no luck.
Manually upgraded to 3.1.2 – this allowed my to login one time and then the problem started occurring again.